Resea ch in o he de elopmen o a T a ic Sa e y Indica o
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Index
INDEX _______________________________________________________ 1
1. PREFACE ________________________________________________ 3
1.1. O igins ............................................................................................................ 3
1.2. Mo i a ion ....................................................................................................... 4
1.3. Scope ............................................................................................................. 5
1.4. P e ious knowledge ....................................................................................... 7
2. PARAMETER DEFINITION __________________________________ 8
2.1. In lux o ehicles (IN) ...................................................................................... 9
2.2. Densi y o ehicles (DE) ............................................................................... 10
2.3. Lane changes (LC) ....................................................................................... 12
2.4. Typology o ehicle dis ibu ion (TD) ............................................................ 13
2.5. A e age speed (AS) ..................................................................................... 14
2.6. Speed s anda d de ia ion (SD) .................................................................... 16
2.7. A e age longi udinal dis ance among ehicles (AD) .................................... 17
2.8. Longi udinal dis ance among ehicles s anda d de ia ion (DD) ................... 19
2.9. A e age la e al dis ance among ehicles (LT) ............................................. 20
2.10. Road we ness (RW) ..................................................................................... 23
2.11. Road isibili y (RV) ....................................................................................... 24
3. TSI INDEX DEFINITION ____________________________________ 25
3.1. Fi s pa ame e s disca ded ........................................................................... 25
3.2. Candida e pa ame e s combina ion ............................................................. 27
3.3. Combina ion quan i ying ............................................................................... 29
3.4. Combina ion no malizing .............................................................................. 31
3.5. S udy cases .................................................................................................. 34
3.6. TSI unc ion de ini ion ................................................................................... 42
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4. APPLICATIONS __________________________________________ 43
4.1. Sa e y anges o he index ........................................................................... 44
4.2. Ma ke ing s a egy ....................................................................................... 45
4.3. Long e m goals ........................................................................................... 46
5. EPILOGUE ______________________________________________ 47
5.1. Conclusions ................................................................................................. 47
5.2. G ee ings ..................................................................................................... 48
5.3. Bibliog aphy ................................................................................................. 49
Resea ch in o he de elopmen o a T a ic Sa e y Indica o
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1. P e ace
1.1. O igins
T a ic Sa e y Indica o p ojec is a small pa o a la ge p ojec ha is been ca ied ou du ing
he las yea s in he Na ional Taiwan Uni e si y o Science and Technology Indus ial
Managemen Depa men , called Sma Campus. This wide p ojec in ol es lo s o
applica ions a ound he campus, and e en a ound he ci y. This p ojec y o apply echnology
in di e en ways o make s akeholde s li es easie by s udying he human low, epo ing
main enance p oblems o ying o imp o e ene gy consump ion, o ins ance.
NTUST is one o he mos impo an uni e si ies in Taiwan and has a e y good epu a ion in
e ms o echnology. In he las yea s, NTUST Cen e o IoT Inno a ion has been wo king ha d
in all kind o In e ne o Things echnologies like: deep lea ning, image ecogni ion, block chain,
senso echnology, e c. In he Figu e 1 i is shown a slide o one p esen a ion abou his p ojec .
P o esso Shuo-Yan Chou, as di ec o o his hesis, p oposed his and some o he p ojec s o
me. A e some esea ch abou hem, ‘T a ic Sa e y Indica o ’ was he selec ed one o
esea ch in o.
In his case, as he p ojec would be applied on ex e nal o uni e si y a ic sa e y, his is a
opic mo e close o Sma Ci y concep . Apa om his one, he e a e se e al p ojec s applied
o Sma Ci y inside Sma Campus, like showing use ul in o ma ion abou buses schedules o
p oposing a sha ed pa king model open o he public.
Figu e 1 T a ic Sa e y Sys em in Sma Campus
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1.2. Mo i a ion
In addi ion o my gene al in e es in echnology due o my s udies and conce ns, wha ha e
been explained in he p e ious sec ion is he main elemen ha ca ches my a en ion: helping
people in hei daily li e decisions using he mos cu en echnology.
The way In e ne o Things (IoT) is been applied in many ac i i ies o people’s ou ine (like
when using phone apps, GPS so wa e o home assis an s, be ween o he s) is a eali y ha
all p o essionals in ol ed in echnologies wo ld should no ice i hey ha e no do i ye .
The in e es in his ield o s udies make me exci ed and in e es ed in de eloping his p ojec
and expanding my knowledge in i . So, as an enginee , o wo k in all kind o p ojec s in his
scope i is ewa ding, e en de eloping he less echnical pa o hem.
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1.3. Scope
This p ojec p e ends o de ine a a ic sa e y index. I means ha by ins alling ideo came as
in any kind o oad, his index could be calcula ed aking in accoun some pa ame e s wi h help
o objec ecogni ion echnology and da a ex ac ing.
The e a e some ideo came as ins alled a NTUST Uni e si y ocused on he s ee . Thanks
o objec ecogni ion echnology, hey a e able o gene a e da a abou a ic as posi ion, speed
and ypology o each ehicle on hei ision ield. Then, da a iles abou a ic will be gene a ed
con inually. In pa allel o his, i is needed o ind he way o make his da a use ul: deciding
which da a is ele an o de ine he sa e y o a oad and he way o do i . Fo his, some
pa ame e s a e needed o be desc ibed o hen make up a unc ion model ha combining
hem gi e sa e y in o ma ion as a esul , and his is p ecisely he scope o his hesis.
Pa allel echnical wo k o achie e ge ing use ul a ic da a om ideo came as is aking o
g an ed in his ideal scena io. I means ha he way da a is ob ained and dealing wi h came a
issues does no in ol e his hesis. I is also assumed ha came as a e loca ed in s a egic
places whe e he cap u ed da e is no in luenced by ex e nal ac o s. In addi ion, i mus be
bo ne in mind ha he da a a e pu ely om a ic, i is no possible o ake in o accoun aspec s
such as he consump ion o alcohol and d ugs, o o he kind o possible dis ac ions o he
d i e s ha canno be cap u ed in a ideo ile.
The e o e, supposing his idyllic si ua ion in which ideo ile can be ex ac ed and u ned in o
all he necessa y da a equi ed, his hesis speci ic goals shown in Figu e 2 a e o de ine and
quan i y pa ame e s and o build he model o calcula e T a ic Sa e y Indica o unc ion.
Figu e 2 Thesis scope in p ojec ou line
Bu his de ini ion mus be in a e y clea and exhaus i e way. The e o e, is also necessa y o
quan i y his pa ame e s, his is o de ine he way hey a e going o be measu ed. La e , a e
s udying di e en op ions, decide which non- e y ele an o non-well quan i ied pa ame e s
can be ejec ed and which mos ep esen a i e o hem will emain as candida es.
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Once pa ame e s a e clea ly de ined and quan i ied, nex s ep would be o de ine he unc ion:
deciding he way o combine he inpu s (pa ame e s) o ake he ou pu (indica o ). P obably,
he e will be some in e medium pa ame e s coming om ce ain i s pa ame e s, ha
combined will gi e as a esul he TSI index.
Final pa ame e s unc ion will conside should be adap ed o he unc ion by no malizing. Fo
each o hem, he e will be a scale be ween 0 and 1: he sa es si ua ion will be always
ep esen ed by numbe 0 and he mos dange ous by numbe 1. Same happens o inal
indica o , hey will show he sa e y o he oad wi h a 0 o 1 scale.
When his goals has been achie ed and his echnology has been es ed, he e will be many
applica ion o ha index. Then, i would be necessa y o collabo a e wi h di e en companies
o o ganiza ions in e es ed on he indica o de eloping o usabili y. I could be used by he
go e nmen in e ms o acciden educ ion, o by ci izens o ge in o med o oads sa e y and
decide a way o hei des ina ion.
This p ojec is ac ually on a pilo phase, so we a e jus building he basis o he index in a
simple and gene ic way. Bu in a medium e m u u e i would be possible o imp o e he index
by inco po a ing use ul conclusions ex ac ed om c ash ideos analysis, among o he s.
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1.4. P e ious knowledge
This p ojec has wo e y di e en pa s: he echnical one and he analy ical one (‘Resea ch
in o he de elopmen o a T a ic Sa e y Indica o ’). The i s o hem, is esponsible o
ex ac ing da a om he ideo came a iles using objec ecogni ion echnology, while he
second one needs o ake ad an age o his da a o con e i in o use ul in o ma ion, de ining
and combining some pa ame e s o analyze a ic sa e y. 10 11 13
My p e ious knowledge o he echnical pa is almos inexis en , and i is no eally necessa y
o de eloping he second one, because i can be done supposing da a ex ac ed p ope ly.
E en so, i was so in e es ing o assis o a class abou ‘Deep lea ning’ impa ed by Richa d,
one o he membe s o he Indus ial Managemen depa men in NTUST. Thanks o ha , i
was possible o lea n some concep s abou he wo k behind he echnical pa and wha a e
hey wo king wi h.
The impo an poin is ha came as a e he mos powe ul senso s ha echnology ha e
de eloped since nowadays. The e a e lo s o speci ic senso s ha allow us knowing speci ic
in o ma ion abou he en i onmen , bu once objec ecogni ion echnology has been
de eloped, came as a e able o p o ide us mo e in o ma ion a he same ime and wi hou
human supe ision han any senso e e de eloped.
Anyway, he impo an pa o his hesis is he second one: how o make da a use ul o
de e mine a ic sa e y. Fo doing i , is e y impo an o de ine he pa ame e s ha a e going
o be used in a clea way, be o e quan i ying and combining hem o ge he sa e y indica o .
Some use ul p e ious knowledge o he p og ess o he p ojec is ela ed o combina ional isk
analysis, lea ned a uni e si y p e ious s udies. Bu he e will be also ha d wo k on ex e nal
esea ch abou his opic14 15. Besides, using common sense and ma hema ical skills will be
necessa y o de ine each pa ame e and he indica o unc ion in a easonable and s ic way.
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2. Pa ame e de ini ion
In his chap e , di e en possible impo an pa ame e s a e going o be de ined and quan i ied.
I is impo an o do a good and exhaus i e de ini ion o each o hem o ensu e i hey a e
ele an o no , and es ablish how o quan i y hem 4.
Some p e ious commen s abou necessa y assump ions o aking in o accoun in he
pa ame e de ini ion a e lis ed below:
Nowadays, came as like he one shown in Figu e 3 a e ge ing some use ul
in o ma ion, bu as old p e iously, i would be supposed an idyllic scena io in which
we could ge all he in o ma ion we wan abou he a ic si ua ion om ideo iles.
Fo a non-in luenced analysis i is impo an o loca e he came as whe e he a ic
is luen , meaning, no close o in e sec ions o a ic ligh s. In his way he a ic will
be analyzed ai ly o each oad, based on pa ame e s alien om in luence o his
ac s. As old in he p e ace, deciding he came a loca ion o he ocus o he
came as does no in ol e his hesis, i is assumed ha hey simply p o ide us he
in o ma ion ha we need.
As i will be shown in he ollowing pages, some o he pa ame e s need he
p esence o a leas 1 ehicle du ing he las n minu es o be calcula ed, so hey
canno be aken in o accoun in he sa e y analysis. This is he case o he
pa ame e s TD, AS, SD, AS and DD. I will be explained la e , bu LT has a mo e
special condi ion o be calcula ed. Fu he mo e, wi h a low p esence o ehicles, he
alue o he pa ame e s is no signi ican .
Fo his eason, i has been decided ha when he densi y (DE) o ehicles is unde
a ce ain limi alue (DE < DE limi ), he index will no be calcula ed and i will be
e u ning 0 as esul . This densi y limi should be de ined once he sys em has been
gene a ing da a and his da a has been con enien ly analyzed.
Figu e 3 T a ic came a
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2.1. In lux o ehicles (IN)
Thanks o image ecogni ion, his is one o he easie pa ame e s o ob ain. Video came as a e
able o de ec and coun he numbe o ehicles passing h ough i s isual camp in a closed
pe iod o ime. Ini ially, a oad wi h lo s o ehicles pe minu e will be less sa e han o he one
wi h ba ely a ic, bu i would be necessa y o analyze in e ac ion wi h o he pa ame e s
This pa ame e will be measu ed in numbe o ehicles pe minu e pe lane. The in lux o
ehicles alue conside ed will be an a e age o he las n minu es da a gene a ion. So, he
numbe o ehicles ha has passed in he las n minu es di ided by n and by he numbe o
lanes o he oad will de ine he a e age in lux o he oad wi h a decimal alue.
𝐼𝑁=𝑁𝑉
𝑛 × 𝑁𝐿 [1]
IN: a e age in lux on came a’s isual ield du ing he las n minu es [ ehicles/min. lane]
NV: numbe o ehicles de ec ed du ing las n minu es [ ehicles]
NL: numbe o lanes on he oad [lanes]
I is ele an o ake in o accoun he numbe o lanes when conside ing he in lux. I is no he
same 100 ehicles pe minu e absolu e in lux in a 1 lane s ee in he ci y cen e ha a 100
ehicles pe minu e in lux in a 5 lanes highway. I will be e y impo an o use he numbe o
lanes s a ic pa ame e o con e absolu e da a in ela i e da a, meaning in his case o al in lux
o in lux pe lane. Same will happen wi h o he pa ame e s we will see in he ollowing pages.
Fo example, i he came a in he ele a ed oad in on o NTUST Uni e si y (Jilonglu Ele a ed
Road) no heas di ec ion, has de ec ed 464 ehicles passing h ough i s 2 lanes (NL = 2) in
he las n minu es, he a e age in lux pa ame e will ake a alue o : IN = 232/n.
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2.6. Speed s anda d de ia ion (SD)
Speed dispe sion o he ehicles is p obably mo e impo an han speed a e age. In his case
we a e alking abou a pa ame e ha has sense by i sel , wi hou need o combining. Meaning,
when all he ehicles ha e simila speeds, he a ic is mo e homogenous and he si ua ion
use o be sa e han when some o hem a e d i ing as e han o he s.
Fo measu ing i , he s anda d de ia ion o all ehicles ha ha e passed h ough he isual
ield o he came a in he las n minu es will be aken in o accoun . Each o hem will ha e an
a e age speed associa ed. Conside ing as many speeds as ehicles, a sample o da a is
ob ained. The s anda d de ia ion o his sample will be conside ed as he speed dispe sion o
he a ic si ua ion.
As shown in he legend o he o mula [8] below, he s anda d de ia ion has he same uni s o
measu emen han he main a iable. In his case, as s anda d de ia ion o speed, i is
kilome e s pe hou , because he main alue is he a e age speed o he ehicles.
𝑆𝐷=√∑(𝐴𝑆𝑖−𝐴𝑆)2
𝑖=𝑁𝑉
𝑖=0 𝑁𝑉 [8]
SD: speed s anda d de ia ion du ing las n minu es [km/h]
ASi: a e age speed o ehicle i [km/h]
AS: a e age speed du ing las n minu es [km/h]
i = (0,…,NV): ehicle
NV: numbe o ehicles de ec ed du ing las n minu es [ ehicles]
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2.7. A e age longi udinal dis ance among ehicles (AD)
The dis ance wi h he ehicle in on is always impo an o a ic sa e y. Tha is why in
highways is ecommended o d i e lea ing a leas 70 me e s o dis ance. I he oad is no a
high speed one, his limi use o be lowe . So, i is in ui i e hinking abou combining a e age
dis ance and speed.
This pa ame e is conside ing dis ance in he a ic di ec ion be ween ehicles in he same
lane. To ob ain a ep esen a i e alue, he a e age o he las n minu es will be conside ed.
This alue will ha e me e s as measu emen uni .
Figu e 6 Longi udinal calcula ing dis ance scheme
In he Figu e 6, he e olu ion o a a ic si ua ion is shown in 4 di e en ins an s. The blue
squa e indica es he came a’s isual ield. Dis ances aking in o accoun by he sys em in each
momen a e ma ked in ed. Con inued lines a e used i bo h ehicles a e seen by he came a.
I can occu , ha wo consecu i e ehicles in he same lane a e no in he isual ield a he
same ime empo ally, o e en in any momen because hey a e d i ing wi h long dis ance
When he i s one lea es he isual ield, he sys em will calcula e he dis ance based on speed
and ime while he second ehicle is s ill in he isual ield o he came a. These dis ances
calcula ed by he sys em a e ma ked in dashed lines in he Figu e 6.
Each ehicle en e ing in he s udy a ea has an assigned ehicle ( he immedia e be o e in he
same lane) wi h which he dis ance is going o be conside ed (like d3 dis ance in he ou h
illus a ion in Figu e 6). So he numbe o pai s o ehicles conside ed will be he same as he
numbe o ehicles de ec ed.
So, o each pai o ehicles, an a e age dis ance will be calcula ed based on hei ins an
dis ance du ing he ime he second one is spending in he s udy a ea:
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𝐴𝐷𝑗=∑𝐼𝐷𝑗𝑡
𝑡=𝑇𝑆𝑗
𝑡=0𝑇𝑆𝑗 ∀ 𝑗 [9]
ADj: a e age longi udinal dis ance be ween he pai o ehicles j [m]
IDj : ins an longi udinal dis ance be ween he pai o ehicles j in he ins an [m]
= (0,…,TSj): ins an ( ime in seconds)
TSj: ime spen by he second ehicle o he pai o ehicles j in came a’s isual ield [s]
j = (0,…,NV): pai o ehicles
NV: numbe o ehicles de ec ed du ing las n minu es [ ehicles]
Then, calcula ing he a e age dis ance o he pai s o ehicles ha ha e passed du ing he las
n minu es, a ep esen a i e a e age longi udinal dis ance is ob ained:
𝐴𝐷=∑𝐴𝐷𝑗
𝑗=𝑁𝑉
𝑗=0
𝑁𝑉 [10]
AD: a e age longi udinal dis ance du ing las nminu es [m]
ADj: a e age longi udinal dis ance o he pai o ehicles j [m]
j = (0,…,NV): pai o ehicles
NV: numbe o ehicles de ec ed du ing las n minu es [ ehicles]
I should be no ed ha al hough he illus a ions ha e used ca s o ep esen ehicles,
e e y hing explained abo e can be ex apola ed o all kind o ehicles.
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2.8. Longi udinal dis ance among ehicles s anda d de ia ion
(DD)
Same as alking abou speed homogenei y, we a e aced wi h a pa ame e ha does ha e
meaning by i sel . The homogenei y o he a ic in e ms o dis ance is a ep esen a i e ac
abou sa e y. As occu s wi h speed, s anda d de ia ion is going o be used o e alua e he
homogenei y o he longi udinal dis ance among ehicles.
Fo measu ing he s anda d de ia ion, e e y ehicle ha ha e passed h ough he isual ield
o he came a will ha e an associa ed dis ance un il he ehicle in on in he same lane, as
shown in he p e ious pa ame e (AD). Associa ed dis ances o each pai o ehicles in he
las n minu es will be used as a sample o calcula e he s anda d de ia ion.
𝐷𝐷=√∑(𝐴𝐷𝑖−𝐴𝐷)2
𝑗=𝑁𝑉
𝑗=0 𝑁𝑉 [11]
DD: longi udinal dis ance s anda d de ia ion du ing las n minu es [m]
ADj: a e age longi udinal dis ance be ween he pai o ehicles j du ing las n minu es [m]
AD: a e age longi udinal dis ance du ing las n minu es [m]
j = (0,…,NV): pai o ehicles
NV: numbe o ehicles de ec ed du ing las n minu es [ ehicles]
As happened in he case o SD pa ame e , s anda d de ia ion has he same measu emen
uni s han he main a iable. So, as we a e in on o a dis ance de ia ion, i s uni s a e me e s.
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2.9. A e age la e al dis ance among ehicles (LT)
La e al dis ance be ween ehicles is one he mos di icul pa ame e o conside . When wo
ehicles a e d i ing in he same lane, conside ing la e al dis ance do no make sense. When
hey a e d i ing in di e en lanes bu wi h a big longi udinal dis ance, nei he . Same happens
when hey a e d i ing in no con iguous lanes. So, his pa ame e has sense i and only i wo
ehicles a e d i ing in con iguous lanes and no e y a longi udinally o when o e lapping
la e ally. 9
Wi h help o he ollowing Figu e 7, i would be easie o unde s and his condi ions mo e
clea ly:
Figu e 7 La e al dis ances condi ions scheme
Abou he ele ance o la e al dis ance (ma ked in blue) in he Figu e 7:
Dis ances be ween ca s 2 and 4 is no ele an because hey a e d i ing in he same
lane.
Dis ances be ween ca s 1 and 2 is no ele an because hei longi udinal dis ance
is big enough.
Dis ances be ween ca s 2 and 5 is no ele an because hey a e no d i ing in
con iguous lanes.
Dis ances be ween ca s 3 and 4 is ele an because hei longi udinal dis ance is
no big enough.
Dis ances be ween ca s 2 and 3 is ele an because hey a e o e lapping
longi udinally (wha means nega i e dis ance)
Now, i is necessa y o de ine he limi longi udinal dis ance o conside he la e al dis ance, bu
i depends on he speed o he back ehicle.
A easonable es ic ion o delimi a e dis ance be ween on pa o back ehicle and back pa
o on ehicle could be he ollowing:
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𝑙𝑑 (𝑚)< 𝑠 (𝑘𝑚/ℎ)
10 [12]
ld: longi udinal dis ance in me e s be ween he pai o ehicles [m]
s : back ca speed in kilome e s pe hou when en e ing in came a’s isual ield [km/h]
Then, i he speed is 50 km/h, la e al dis ance will be only calcula ed i he longi udinal dis ance
is less han 5 me e s; and i he speed is 120 km/h, i i is less han 12 me e s.
Figu e 8 La e al dis ance es ic ion scheme
In he example in he Figu e 8, la e al dis ance (0,75 m) would be conside ed because
longi udinal dis ance (1,25 m) is lowe han he limi dis ance o 25 km/h (2,50 m).
Thus, la e al dis ance be ween 2 ehicles will be conside ed i and only i hei longi udinal
dis ance is lowe han he limi one o he co esponding speed. Wi h he dis ances calcula ed
o each pai o ehicles has passed h ough he isual ield o he came a du ing las n minu es
ha mee his es ic ion, a sample o da a is gene a ed.
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Wi h ha sample a la e al a e age dis ance be ween ehicles is calcula ed:
𝐿𝑇=∑𝐿𝑇𝑘
𝑘= 𝑃𝑅
𝑘=0
𝑃𝑅 [13]
LT: a e age la e al dis ance du ing las n minu es [m]
LTk: a e age la e al dis ance o he pai o ehicles k [m]
k = (0,…,PR): pai o ehicles accomplishing he es ic ion
PR: pai s o ehicles du ing las n minu es ha accomplish he es ic ion [ ehicles]
As old in he in oduc ion o pa ame e de ini ion, he case o LT is special. Fo calcula ing his
pa ame e is necessa y ha wo ehicles ha accomplish he es ic ion has passed h ough
he came a isual ield du ing he las n minu es. This is e en a mo e es ic i e condi ion han
he limi a ion o o he pa ame e s (NV = 0). When eal da a is ob ained by he came as his
pa ame e should be es ed exhaus i ely because o hese eason.
Resea ch in o he de elopmen o a T a ic Sa e y Indica o
23
2.10. Road we ness (RW)
Wea he is ob iously ele an in sa e y. Especially when i is ainy, he a ic become mo e
dange ous. When i is aining o snowing, i is impo an o d i e e en in a mo e cau ious way:
so e , wi h less speed and mo e dis ance, e c. Howe e , e alua ing he wea he i is no e y
use ul i i is sunny o cloudy while he loo emains d y. Fac s ha ha e in luence o e he
oad on a ic sa e y is p ecipi a ion: ain o snow.
Fo he ime being, i is going o be supposed ha he came as a e able o de ec h ough he
image and p o ide o he sys em a pa ame e abou he condi ions o we ness o he oad. This
pa ame e indica es i he oad is d y o we . I i s alue is 0 i means ha he loo is comple ely
d y and sa e o d i e, while 1 means ha he oad is o ally we , he mos scena io o his
pa ame e (Figu e 9).
Figu e 9 Road we ness scale
RW = [0, 1]: oad we ness pa ame e inc easing om d y o we condi ions
Fo example, when he oad is o ally we du ing a s o m he pa ame e would be loca ed a 1,
a sunny o e en cloudy bu d y day i will be 0, and a cold nigh wi hou ain bu wi h humidi y
i would be maybe a ound RW = 0,3.
Resea ch in o he de elopmen o a T a ic Sa e y Indica o
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2.11. Road isibili y (RV)
Wi h isibili y happens some hing simila ha wi h we ness pa ame e . I can a ec o o he
pa ame e s ange o sa e y. This is, some speed ha can seem sa e wi h good isibili y in a
clea day, could be e y dange ous in a si ua ion o a ainy nigh wi h a lo o og. So, i would
be good o conside his ac in he sa e y index.
Thus, conside ing ha came as can p o ide us some index o isibili y based on he clea ness
o he cap u ed image, his pa ame e is al eady de ined. When i has a alue o 0 i means
ha he condi ions a e comple ely clea and sa e o d i e, while 1 means he wo s isibili y
condi ions (Figu e 10).
Figu e 10 Road isibili y scheme
RV = [0, 1]: oad isibili y pa ame e inc easing om clea o uzzy condi ions
This pa ame e a ies depending on he isibili y signal coming om each came a. I depends
on ac o s like on he wea he (i i is sunny, cloudy, ainy, o especially oggy, like in Figu e
11), he s ee ligh ing and i i is day o nigh .
Figu e 11 Fuzzy oad isibili y condi ions
Resea ch in o he de elopmen o a T a ic Sa e y Indica o
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3. TSI index de ini ion
3.1. Fi s pa ame e s disca ded
Once all possible pa ame e s a e al eady de ined, i is necessa y o decide which o hem a e
going o be used. Fi s s ep is o do a i s il e and disca d some o hem.
This hesis is jus abou he cons uc ion a basis o a pilo unc ion. Al hough is he u u e his
wo k could be inished and imp o ed inco po a ing mo e elemen s and de eloping a mo e
complex analysis, o he momen i is mo e con enien o make i up wi h some clea and
easy o combine pa ame e s han y o use oo much o hem. 5
So he i s ejec ed pa ame e s a e going o be lis ed and explained below:
In lux o ehicles (IN)
The case o pa ame e is kind o special. I has no been ejec ed because o lack o
in o ma ion. Ac ually, he in lux o ehicles gi e us use ul in o ma ion. The p oblem wi h his
pa ame e is ha i has lineal dependence ela ionship wi h o he pa ame e s: densi y and
a e age speed:
𝐼𝑁 [𝑣𝑒ℎ.
𝑚𝑖𝑛]=𝐷𝐸 [𝑣𝑒ℎ.
𝑘𝑚] ×𝐴𝑆 [𝑘𝑚
ℎ]×1
3.600 [ℎ
𝑚𝑖𝑛] [14]
So, using hese h ee pa ame e s a he same ime we would be in ol ed in a si ua ion o
in o ma ion edundancy. Fo his eason, one o hem was needed o be ejec ed, and
analyzing possible combina ions wi h o he pa ame e s, he chosen one was in lux o ehicles.
Typology o ehicle dis ibu ion (TD)
Al hough his pa ame e could be e y use ul in he u u e, i has been conside ed as oo
complex o ake in accoun o he momen . Fo he momen , TD pa ame e is no going o be
used o calcula e he TSI index, bu i is le open o be used in possible u u e imp o emen s
o he indica o .
Resea ch in o he de elopmen o a T a ic Sa e y Indica o
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In o de o consolida e he unc ion, i has been calcula ed o some conside ed sa e y b aking
dis ance o se e al speeds (scena ios om S7 o S12)1:
Table 5 B aking sa e y dis ances es ing (Excel)
S7
S8
S9
S10
S11
S12
AS (km/h)
20
40
60
80
100
120
AD (m)
4
16
36
64
100
144
𝑓(𝐴𝑆,𝐴𝐷)
10,00
10,00
10,00
10,00
10,00
10,00
|𝑓(𝐴𝑆,𝐴𝐷)|
0,25
0,25
0,25
0,25
0,25
0,25
As i shows he Table 5, and as expec ed, o all hese scena ios he unc ion akes he same
alue. I makes sense because he b eaking sa e y dis ances a e hough specially o each
speed, so all o hem a e supposed o be equal in sa e y e ms. As he dis ances a e o b ake
sa ely, he index akes a low alue, wha also makes sense.
A e y common way o no malize his kind o unc ions would be o use speci ic p epa ed
unc ions o i , like o ins ance he ‘logis ic unc ion’ 12 ep esen ed in Figu e 12, in i s gene al
e sion, wi h pa ame e s o egula e:
Figu e 12 Logis ic unc ion g aphic
𝑓(𝑥)=1
1+𝑒−𝑥→𝑓(𝑥,𝑎,𝑚,𝑛,𝑡)=𝑎×1+𝑚×𝑒−𝑥
𝑡
1+𝑛×𝑒−𝑥
𝑡 [18]
Resea ch in o he de elopmen o a T a ic Sa e y Indica o
33
Fo no malizing some pa ame e s, like o example, he densi y o he a ic, his unc ion will
i p ope ly. When a oad is almos emp y, i is no e y impo an i he e a e 0, 1, 2 o 3 ehicles
pe kilome e . Same happens when he oad is o ally collapsed and i s densi y akes e y high
alues. Whe e he di e ence is ele an in sa e y e ms is when he densi y akes in e medium
alues. Then, using an adap ed e sion o he logis ic unc ion would de ini ely make sense.
The e a e many possible me hods o no malize alues using se e al ma hema ical unc ions
o adap alues o pa ame e s o he desi ed ange. Some g aphics a e shown in Figu e 13.
Figu e 13 Se e al no malizing unc ions g aphics
Resea ch in o he de elopmen o a T a ic Sa e y Indica o
34
3.5. S udy cases
Once he pa ame e s ha a e going o in e ene in he index o mula a e al eady no malized,
he unc ion has o be buil . Fo doing his, based on how he isk analysis ha e been his o ically
de eloped 2 3, i has been decided ha he unc ion has o be a p oduc unc ion o he ac o s
o pa ame e s. The e o e, he weigh s o he di e en pa ame e s should be placed as
exponen s.
Th ee possible unc ion models ha e been p oposed, s udied and es ed:
Weigh ed sa e y pa ame e s p oduc :
𝑇𝑆𝐼1=∏( 𝑃𝑛𝛼𝑛 )
𝑛
𝑖=1 [19]
Weigh ed isk pa ame e s (1 – Sa e y) p oduc sub ac ion:
𝑇𝑆𝐼2=1−∏(1−𝑃𝑛)𝛼𝑛
𝑛
𝑖=1 [20]
Weigh ed sa e y pa ame e s sub ac ion p oduc sub ac ion:
𝑇𝑆𝐼3=1−∏(1−𝑃𝑛𝛼𝑛)
𝑛
𝑖=1 [21]
A esume o some o he es s done in he unc ion model selec ion is shown in he nex pages.
The e a e lo s o p e ious es s done in he i s phases o he esea ch ha a e no going o
be shown. These a e jus some o he las s udy cases done wi h p ope alues o he a iables
ha allow us o see he beha io o he unc ions.
Resea ch in o he de elopmen o a T a ic Sa e y Indica o
35
Fo doing hese inal es s, h ee p e ious assump ions ha e been made in his pa icula case:
- The numbe o pa ame e s aken in accoun o he unc ion is 3 (i = 3): P1, P2 and
P3.
- Each unc ion has been es ed o he same 10 hypo he ical scena ios. These
scena ios a e de ined wi h alues o each o he h ee pa ame e s. The alues
assigned y o ep esen and desc ibe se e al a ied cha ac e is ic si ua ions and
combina ions. The alue o he 3 no malized pa ame e s (P1 o P3) o each o he
10 scena ios (S1 o S10) a e shown in Table 6:
Table 6 Pa ame e alues o each scena io (Excel)
P1
P2
P3
S1
0,14
0,07
0,18
S2
0,18
0,11
0,44
S3
0,51
0,17
0,43
S4
0,56
0,39
0,43
S5
0,78
0,44
0,49
S6
0,91
0,5
0,81
S7
0,91
0,88
0,83
S8
0,22
0,19
0,77
S9
0,85
0,15
0,82
S10
0,54
0,76
0,28
- The espec i e weigh exponen s o his 3 pa ame e s depends on each model. As
i will be explained la e , each o he analyzed models equi es a di e en ange o
‘α’ alues. So, in he es s shown in his poin , his has been al eady aken in o
accoun , and ‘α’ alues i wi h he model hey ha e been chosen o . This is, he i s
es s done o s udying he ange o ‘α’ a e no a ached because he alue o he
index was no ele an .
The ollowing Table 7 shows he used exponen s (α1 o α3) o he es s o each
model (TSI1 o TSI3):
Table 7 Alpha alues o each model (Excel)
α1
α2
α3
TSI1
0,21
0,23
0,24
TSI2
0,35
0,4
0,41
TSI3
2,15
2,01
1,9
Resea ch in o he de elopmen o a T a ic Sa e y Indica o
36
Because o he ma hema ical na u e o he models, he ‘α’s’ a e loca ed in di e en
ange o alues o each unc ion, bu in all he cases he weigh gi en o he
pa ame e s is inc easing om P1 o P3 (P1 is he leas impo an , P2 he in e media e,
and P3 he mos impo an pa ame e o any o he h ee unc ions). Anyway, i has
no been wan ed o make a big di e ence in he weigh s o each one.
Bu , as can be seen in he Table 7 numbe s, he ela ionship be ween he alue o he
exponen and he weigh assigned o he pa ame e has no he same beha io o
each model. While in TSI1 and in TSI2, a big alue o ‘α’ means mo e weigh , he
opposi e occu s in he hi d one: he mo e α, he less weigh assigned o he espec i e
pa ame e . This ac is also due o he ma hema ical disposi ion o he a iables on he
di e en models.
Once he p e ious assump ions ha e been p ope ly explained, he 3 unc ions mus be
simpli ied om gene al (TSIX) o speci ic s udy cases (TSIX’)
𝑇𝑆𝐼1′= 𝑃10,21×𝑃20,23×𝑃30,24 [22]
𝑇𝑆𝐼2′= 1 − (1 − 𝑃1)0,38×(1−𝑃2)0,40×(1−𝑃3)0,41 [23]
𝑇𝑆𝐼3′= 1 − (1−𝑃12,15)×(1−𝑃22,01)×(1−𝑃31,90) [24]
Resea ch in o he de elopmen o a T a ic Sa e y Indica o
37
He e below a e some o he esul s ob ained in he es s, and some conclusions ex ac ed om
hei analysis:
Re u ned esul s o he i s unc ion es ing wi h he speci ica ions p e iously
explained (Table 8):
Table 8 Fi s model (TSI1’) e u ned alues (Excel)
TSI1
P1^α1
P2^α2
P3^α3
TSI1
S1
0,6617
0,5425
0,6626
0,2379
S2
0,6976
0,6019
0,8212
0,3448
S3
0,8681
0,6653
0,8166
0,4717
S4
0,8854
0,8053
0,8166
0,5822
S5
0,9492
0,8279
0,8426
0,6622
S6
0,9804
0,8526
0,9507
0,7947
S7
0,9804
0,9710
0,9563
0,9104
S8
0,7276
0,6825
0,9392
0,4664
S9
0,9664
0,6464
0,9535
0,5957
S10
0,8786
0,9388
0,7367
0,6077
TSI1 es conclusions:
- By simply mul iplying he se e al ac o s (wi hou exponen s) he ob ained alue o
he index a e oo low, because he pa ame e s a e no malized om 0 o 1.
- When he exponen s a e in oduced o weigh he di e en pa ame e s, i hey a e
g ea e han 1 his p oblem ge s wo se.
- By in oducing weigh exponen s smalle han 1, he unc ion seems o e u n mo e
easonable esul s.
- Bes esul s a e ob ained wi h exponen s wi h alues a ound 0,15 and 0,3 (Table 8),
bu hey a e oo high when he pa ame e s ake low alues ( o example S1 and S2).
- In gene al, especially o ex eme pa ame e alues, his unc ion show oo mode a e
alues o he index
- This unc ion is ejec ed because e en wi h he mos sui able exponen s, i doesn’
ha e he expec ed beha io o some scena ios
Resea ch in o he de elopmen o a T a ic Sa e y Indica o
38
Re u ned esul s o he second unc ion es ing wi h he speci ica ions
p e iously explained (Table 9):
Table 9 Second model (TSI2’) e u ned alues (Excel)
TSI2
(1-P1)^α1
(1-P2)^α2
(1-P3)^α3
TSI2
S1
0,9486
0,9714
0,9219
0,1506
S2
0,9329
0,9545
0,7884
0,2980
S3
0,7791
0,9282
0,7942
0,4257
S4
0,7503
0,8206
0,7942
0,5111
S5
0,5886
0,7930
0,7588
0,6458
S6
0,4305
0,7579
0,5062
0,8349
S7
0,4305
0,4282
0,4836
0,9108
S8
0,9167
0,9192
0,5474
0,5388
S9
0,5148
0,9371
0,4951
0,7612
S10
0,7620
0,5650
0,8740
0,6237
TSI2 es conclusions:
- In his case, o be mo e cohe en wi h a isk analysis, he unc ion wo ks wi h
dange / isk (1 – P) ins ead wi h sa e y (P).
- Now, he p oblem is he opposi e: he unc ion is e u ning oo high alues when
es ing wi hou exponen s.
- Regula ing he unc ion by in oducing he exponen s, i hey a e smalle han 1, he
esul s a e e en bigge .
- When using exponen s bigge han 1, he e u ned alues seem o be be e .
- Bes esul s a e ob ained wi h exponen s wi h alues a ound 0,3 and 0.5 (Table 9),
bu he e a e s ill a p oblem wi h low pa ame e alues, al hough he si ua ion has
imp o ed conside ably.
- In gene al, especially o ex eme pa ame e alues, his unc ion show oo mode a e
alues o he index
- The unc ion is conside ed accep able, bu i is needed o be compa ed wi h ano he
al e na i e
Resea ch in o he de elopmen o a T a ic Sa e y Indica o
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Re u ned esul s o he hi d unc ion es ing wi h he speci ica ions p e iously
explained (Table 10):
Table 10 Thi d model (TSI3’) e u ned alues (Excel)
TSI3
1-P1^α1
1-P2^α2
1-P3^α3
TSI3
S1
0,9854
0,9952
0,9615
0,0570
S2
0,9749
0,9882
0,7898
0,2391
S3
0,7649
0,9716
0,7988
0,4063
S4
0,7125
0,8493
0,7988
0,5166
S5
0,4139
0,8080
0,7421
0,7518
S6
0,1835
0,7517
0,3299
0,9545
S7
0,1835
0,2266
0,2981
0,9876
S8
0,9614
0,9645
0,3914
0,6371
S9
0,2949
0,9779
0,3141
0,9094
S10
0,7341
0,4240
0,9110
0,7165
TSI3 es conclusions:
- By eloca ing he exponen , we ob ain he p oduc o 1 minus pa ame e o some
powe , ins ead o simply a alue o a powe . This makes mo e sense and has
mo e complexi y bu also be e cha ac e iza ion.
- Wi hou conside ing exponen s (wi h α = 1) he esul s a e exac ly he same as in
TSI2.
- S udying he beha io o he unc ion wi h di e en exponen s, i hey a e smalle
han 1, he unc ion akes alues e en highe .
- Tes ing α > 1 he index akes mo e easonable alues, especially wi h exponen s
a ound 1,75 and 2,25 (Table 10).
- In his case he objec i e o educe he index alues o lowe pa ame e alues is
eached, and he unc ion has also a good beha io o all pa ame e anges.
- The objec i e o ex eme esul s in case o big pa ame e s alues is also eached.
Resea ch in o he de elopmen o a T a ic Sa e y Indica o
40
O he gene al es conclusions:
- TS1 e u ns 0 i one o he pa ame e s is 0. Ne e heless, TSI2 and TSI3 e u n 1 i
he e is a pa ame e ha is 1. Tha occu s because o he ma hema ical eason
ha 0 mul iplied by any numbe gi es 0 as esul .
This umina ion is he ex eme case, bu in gene al, TSI1 is a unc ion ha (wi hou
using exponen s o egula e) gi e always lowe alue o he index han TSI2 and
TSI3 do o same pa ame e alues. This means ha TS1 ell us ha he si ua ion
is sa e han TSI2 and TSI3 do. Fu he mo e, TSI2 y TSI3 akes he same alue
wi h all he exponen s equal o 1.
- I is also impo an o highligh ha TSI3 use o gi e mo e ex eme alues. This is,
when all he pa ame e s a e high, he index alue gi en by TSI3 is bigge han
hose gi en by he o he wo models. And wi h low pa ame e s alues is also TSI3
he one ha gi es he lowes index. Ac ually, his is one o he mul iple easons
why TSI3 is conside ed he mos con enien unc ion.
In he ollowing Table 11 and in Figu e 14 g aphic, he TSI alue ob ained wi h each unc ion
is ep esen ed. The scena ios ha e been o de ed om mo e dange ous o mo e sa e (based
on he TSI3 c i e ia) o a be e isualiza ion in he g aphic:
Table 11 Re u ned alues o each model (Excel)
TSI1
TSI2
TSI3
S7
0,91035
0,91085
0,98760
S6
0,79469
0,83486
0,95448
S9
0,59565
0,76119
0,90941
S5
0,66219
0,64582
0,75183
S10
0,60773
0,62368
0,71645
S8
0,46642
0,53875
0,63706
S4
0,58223
0,51107
0,51658
S3
0,47166
0,42574
0,40634
S2
0,34479
0,29798
0,23907
S1
0,23786
0,15056
0,05701
Resea ch in o he de elopmen o a T a ic Sa e y Indica o
41
Figu e 14 TSI alues e u ned lines g aphic (Excel)
As he o ange line in Figu e 14 indica es, TSI2 so s he 10 scena ios in he same o de han
he TSI3 (g ey line) does. The di e ence be ween hese wo models esides in ha TS2 gi es
mo e mode a e alues han TSI3. Analyzing he scena io S7, ha is he mos dange ous o
he p oposed, we can see ha he h ee pa ame e s a e bigge han 0,8, wha means ha he
a ic is qui e dange ous o h ee di e en easons. When some hing like his occu s, i means
ha he gene al sa e y si ua ion is e y ala ming, because in his case, he 3 conside ed as
mos impo an pa ame e s a e all showing dange . Same happens wi h sa es si ua ions (like
scena io S1), i all he pa ame e s indica es sa e y o di e en easons, i has o be
con enien ly e lec ed in he global TSI index.
Howe e , as is shown by he blue line in Figu e 14, TSI1 so he scena ios in a di e en way.
This is caused o he ac ha TSI1 is ope a ing di ec ly wi h he sa e y pa ame e alues (P)
y ins ead o he isk (1 - P). As explained in he ‘TSI2 es conclusions’ in S udy cases poin , in
his kind o analysis is con enien o wo k mul iplying isks, a he han sa e y. This is because
when mul iplying no malized ac o s, he ma hema ical endency o inclina ion is o app oach
o 0 (sa e y). Bu when a ic sa e y is analyzed, one sa e pa ame e canno camou lage high
alues o o he s.
To conclude his chap e , i has o be said ha he model ha is going o be used he eina e
is TSI3.
Resea ch in o he de elopmen o a T a ic Sa e y Indica o
48
5.2. G ee ings
This hesis and his au ho hope ha his is jus a basis ha gi e suppo o u u e con ibu o s
in he cons uc ion o a use ul p oduc ha helps o people in hei daily li e and also o he
wel a e and ci izen secu i y.
I would especially like o hank he help o he P o esso Shuo-Yan Chou, who ga e me he
oppo uni y o pa icipa e in one o he inno a i e p ojec in which he depa men is in ol ed.
He has also suppo ed me wi h a high quali y ad iso y, especially in he de ini ion o he
pa ame e s and he unc ion model designing, bu also in he de elopmen o he p ojec in
gene al. He has been able o guide he e olu ion o his wo k in a e y p o essional way hanks
o his en iable and espec able expe ience.
Likewise, I would like o hank he people who suppo me in my daily li e in e e y hing I emba k
on bo h pe sonal and p o essional, my amily, gi l iend and iends who ha e also indi ec ly
collabo a ed as in e e y hing I do: encou aging me
Thanks o all o hem.
Resea ch in o he de elopmen o a T a ic Sa e y Indica o
49
5.3. Bibliog aphy
[1] Expe oau o ecambios.es (2017): ‘Calcula la dis ancia de enado co ec amen e –
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